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Register a new userMagnitude Bounded Matrix Factorisation for Recommender Systems
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Low rank matrix factorisation is often used in recommender systems as a way of extracting latent features. When dealing with large and sparse datasets, traditional recommendation algorithms face the problem of acquiring large, unrestrained, fluctuating values over predictions especially for users/items with very few corresponding observations. Although the problem has been somewhat solved by imposing bounding constraints over its objectives, and/or over all entries to be within a fixed range, in terms of gaining better recommendations, these approaches have two major shortcomings that we aim to mitigate in this work: one is they can only deal with one pair of fixed bounds for all entries, and the other one is they are very time-consuming when applied on large scale recommender systems. In this paper, we propose a novel algorithm named Magnitude Bounded Matrix Factorisation (MBMF), which allows different bounds for individual users/items and performs very fast on large scale datasets. The key idea of our algorithm is to construct a model by constraining the magnitudes of each individual user/item feature vector. We achieve this by converting from the Cartesian to Spherical coordinate system with radii set as the corresponding magnitudes, which allows the above constrained optimisation problem to become an unconstrained one. The Stochastic Gradient Descent (SGD) method is then applied to solve the unconstrained task efficiently. Experiments on synthetic and real datasets demonstrate that in most cases the proposed MBMF is superior over all existing algorithms in terms of accuracy and time complexity.
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We tackle the problem disentangling the latent space of an autoencoder in order to separate labelled attribute information from other characteristic information. This then allows us to change selected attributes while preserving other information. Our method, matrix subspace projection, is much simpler than previous approaches to latent space factorisation, for example not requiring multiple discriminators or a careful weighting among their loss functions. Furthermore our new model can be applied to autoencoders as a plugin, and works across diverse domains such as images or text. We demonstrate the utility of our method for attribute manipulation in autoencoders trained across varied domains, using both human evaluation and automated methods. The quality of generation of our new model (e.g. reconstruction, conditional generation) is highly competitive to a number of strong baselines.
We present a fast variational Bayesian algorithm for performing non-negative matrix factorisation and tri-factorisation. We show that our approach achieves faster convergence per iteration and timestep (wall-clock) than Gibbs sampling and non-probabilistic approaches, and do not require additional samples to estimate the posterior. We show that in particular for matrix tri-factorisation convergence is difficult, but our variational Bayesian approach offers a fast solution, allowing the tri-factorisation approach to be used more effectively.
Recommender systems are often designed based on a collaborative filtering approach, where user preferences are predicted by modelling interactions between users and items. Many common approaches to solve the collaborative filtering task are based on learning representations of users and items, including simple matrix factorization, Gaussian process latent variable models, and neural-network based embeddings. While matrix factorization approaches fail to model nonlinear relations, neural networks can potentially capture such complex relations with unprecedented predictive power and are highly scalable. However, neither of them is able to model predictive uncertainties. In contrast, Gaussian Process based models can generate a predictive distribution, but cannot scale to large amounts of data. In this manuscript, we propose a novel approach combining the representation learning paradigm of collaborative filtering with multi-output Gaussian processes in a joint framework to generate uncertainty-aware recommendations. We introduce an efficient strategy for model training and inference, resulting in a model that scales to very large and sparse datasets and achieves competitive performance in terms of classical metrics quantifying the reconstruction error. In addition to accurately predicting user preferences, our model also provides meaningful uncertainty estimates about that prediction.
Non-negative Matrix Factorisation (NMF) has been extensively used in machine learning and data analytics applications. Most existing variations of NMF only consider how each row/column vector of factorised matrices should be shaped, and ignore the relationship among pairwise rows or columns. In many cases, such pairwise relationship enables better factorisation, for example, image clustering and recommender systems. In this paper, we propose an algorithm named, Relative Pairwise Relationship constrained Non-negative Matrix Factorisation (RPR-NMF), which places constraints over relative pairwise distances amongst features by imposing penalties in a triplet form. Two distance measures, squared Euclidean distance and Symmetric divergence, are used, and exponential and hinge loss penalties are adopted for the two measures respectively. It is well known that the so-called multiplicative update rules result in a much faster convergence than gradient descend for matrix factorisation. However, applying such update rules to RPR-NMF and also proving its convergence is not straightforward. Thus, we use reasonable approximations to relax the complexity brought by the penalties, which are practically verified. Experiments on both synthetic datasets and real datasets demonstrate that our algorithms have advantages on gaining close approximation, satisfying a high proportion of expected constraints, and achieving superior performance compared with other algorithms.
The embedding-based representation learning is commonly used in deep learning recommendation models to map the raw sparse features to dense vectors. The traditional embedding manner that assigns a uniform size to all features has two issues. First, the numerous features inevitably lead to a gigantic embedding table that causes a high memory usage cost. Second, it is likely to cause the over-fitting problem for those features that do not require too large representation capacity. Existing works that try to address the problem always cause a significant drop in recommendation performance or suffers from the limitation of unaffordable training time cost. In this paper, we proposed a novel approach, named PEP (short for Plug-in Embedding Pruning), to reduce the size of the embedding table while avoiding the drop of recommendation accuracy. PEP prunes embedding parameter where the pruning threshold(s) can be adaptively learned from data. Therefore we can automatically obtain a mixed-dimension embedding-scheme by pruning redundant parameters for each feature. PEP is a general framework that can plug in various base recommendation models. Extensive experiments demonstrate it can efficiently cut down embedding parameters and boost the base models performance. Specifically, it achieves strong recommendation performance while reducing 97-99% parameters. As for the computation cost, PEP only brings an additional 20-30% time cost compared with base models. Codes are available at https://github.com/ssui-liu/learnable-embed-sizes-for-RecSys.
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